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Let q ≥ 2 be an integer and let s q (n) be the sum-of-digitsfunction of n in base q. The function s q (n) has been studied in many directions and many properties have been obtained on the distribution of s q (n) and s q (P (n)) , where P is a suitable polynomial. In this paper we derive the generatingfunctions of s p (n d mod p k) for d ≥ 2 and prime p ≥ 2 by using the properties of Dirichlet character, and study the correlation properties of the sequences ((- 1) n 2 mod p k ) n < p k . [ABSTRACT FROM AUTHOR]